Blitz games are chess games with time limit of 2 minutes+2sec to 10 minutes.
Normal games are chess games with the time limit from 15 minutes to Untimed.
General means the whole ratings you have on Blitz, Bullet, and Normal combined. The general shows your real and "official" rating in ChessCube.
To increase your ratings in one of those 3 categories, just play and win the games in that category. For example, if you want to improve your rating on Blitz, play and win blitz games as much as you can. Improving one category will improve your general rating.